Đề thi thử đại học môn Toán số 19

so crAo DUC vA DAo rAo HA rlxn TNUOxG THPT I{GT]yEn TRUNG THTEx DE Trrr THUDAI rrQC LAt{ rr xAru 2014 Mdn: TOAxt Kh6i A, B, Al (Thoi gian: 180 phft, khdng hO ttroi gian phft aC; r. pnAN cHUNG cHo rAr cA rni srNH 12,0 ai6m) p.ha l1Z,O Ai6m; Cho hdm s6 y = x3 +3x2 - 4 (l) \/ a,Khho s6t sg bi6n thi6n vd vE OO ttri (C) cria ham sO (t) y,(. "no z ai6m ,(!,r),*(:r). vitit phucrng trinh dudng thing I ciit ao ttri (c) tei hai dii5m p, e sao cho tti gi6c MNPQ la hinh binh hdnh. ' X Ji -+"in(r.*I)+2sin4x Ciu2 (1,0 tli6m). Giai phucrng trinh: =2-4cos2x / ""['-;j ^ .V" ^ f*t +l2yz +x+2=8y3 +8/ Cf,u 3. (1,0 tli6m). Giai hQ phucmg trinh: I :- e LJtt * 8y1 +2y =5* nfO" 4. (l,|Ai6m;. Tinh tfch ph6n: t ="[ffia. u/ c6u 5. (1, 0 tli6m). Cho hinh ch6p s.ABCD.c6 d6y ABCD la hinh thoi canh bang a (a>0), AC : a. Tam gi6c QAB cQn t4i S vd nim trong m4t phing vudng g6c v6i mlt ddy; g6c eitra SC v6i *at pttittg (AB!D) bing 600. Ggi I ld trung ai6- cfla AB. iiott ttr-c ii.h r,iu nroi .itop's. i,ecn vd khoang cricf, tL Aiem t ei5n m{t phEng (SBC) theo a. Ciu 6 1f,O AiOm;. Cho c6c s6 thgc duong X, y, zthbamdn: *' * y' + z2 + xy + yz + zx 2. Chimgminh ring: r' *!,u * r" *!,, * r'* !!r r-3 \x + y)' (y + z)" (z + x)" rf, PHAN nftNC 1f,O AiOml. Thf sinh chi tlugc lim mQt trong hai phAn (A hoic B). t ,{, fheo chrong trinh Chudn Wq Ta (1,0 tli6m). Trong m4t phing tga dQ Oxy. Cho tam gi6c ABC vudng t4i A. Phucrng trinh ducmg 1.hi"g BC ld 4x -3y - 4 = 0; c6c di6n A, B thuQc tryc hodnh vd diQn tich tam gi6c ABC biig 6. fim tgi i,/dOtrgng tdm G cta tam gi6c ABC. V Ceu 8a (1, 0 tli6m). .Trong kh6ng gian vdi hQ tga dQ Oxyz, cho hai rli6m A(1;1;t) vd B (0; 2;2).Viet ghucrng trinh m{t phing (P) di qua A, B il6ng thdi (P) "6t o*, oy lAn luqr taitrai Aicm ph6n ti-ci vt, N fM, N khdng trung vdi O) sao cho OM:2ON. t / r t " , / ly \U/cau 9a (1,0 tti6m). Tim h9 s5 cria sti h4ng chfa x5trong khai triiSn Niutcrn t;-i| , uitit raog ['i +Clu+zc: = 4, neZ* B. Theo chwong trinh Nfrng coo Cdu 7b (1, 0 tli6m). Trong mat phang vdi hQ tqa d0 Oxy, cho hai ducmg trdn (q) :x2 +(y+t)z =4 u6 (cr):(x-l)'+ f2 =2. vii5t phucrng trinh dulng thdng A, bii5t A titip xric v6i (Cr) vd A^ cgt (Cz tai hai tli€m phdn biet AB sao cho AB :2. Ciu 8b (1, 0 tli6m). Trong kh6ng gian v6i hQ tga dQ Oxyz, cho hai duOrng thAng: A, ,; = + = T uU . x-I v-( A ' r- -J t-=' Timili6mAt6nA1,Bt6nA2saochodudrngthAngABdiquadi€mM(1;9;0). ll^ 't 2-l Ciu 9b (1,0 tli6m). Tirc6c,cht sO 1,2,?,4,5,6.Vi6t ngSu nhi€n mQt st5 Lu nhiOn g6m 4 cht s6 it6i mQt khric nhau. Tfnh x6c suSt dc vir5t du-ry. c so qr ntricn sa9 cho trong mdi si5 d6 ph6i .o -At cht s6 I vd2. .HET- Hp vd tAn thf sinh . +3x2 - 4 (l) / a,Khho s6t sg bi6n thi6 n vd vE OO ttri (C) cria ham sO (t) y,(. "no z ai6m ,(!,r),*(:r). vitit phucrng trinh dudng thing I ciit ao ttri (c) tei hai